What is the derivative of x^{4/5}(x-2^2) ?

The derivative of x^{4/5}(x-2^2) is (14x^2-36x+16)/(5x^{1/5)}

What is the first derivative of x^{4/5}(x-2^2) ?

The first derivative of x^{4/5}(x-2^2) is (14x^2-36x+16)/(5x^{1/5)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x^{\frac{4}{5}} (x - 2)^{2})

\frac{14 x ^{2} - 36 x + 16}{5 x ^{\frac{1}{5}}}

Solution steps

\frac{d}{d x} (x^{\frac{4}{5}} (x - 2)^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{4}{5}}, g = (x - 2)^{2}

= \frac{d}{d x} (x^{\frac{4}{5}}) (x - 2)^{2} + \frac{d}{d x} ((x - 2)^{2}) x^{\frac{4}{5}}

\frac{d}{d x} (x^{\frac{4}{5}}) = \frac{4}{5 x ^{\frac{1}{5}}}

\frac{d}{d x} ((x - 2)^{2}) = 2 (x - 2)

= \frac{4}{5 x ^{\frac{1}{5}}} (x - 2)^{2} + 2 (x - 2) x^{\frac{4}{5}}

Simplify

\frac{4}{5 x ^{\frac{1}{5}}} (x - 2)^{2} + 2 (x - 2) x^{\frac{4}{5}} : \frac{14 x ^{2} - 36 x + 16}{5 x ^{\frac{1}{5}}}

= \frac{14 x ^{2} - 36 x + 16}{5 x ^{\frac{1}{5}}}

\frac{d}{d x} (\frac{( x ^{2} )}{1 + x})

x \to \frac{π}{2} lim (3 sec (x))

\int \frac{tan ( x )}{sin ( 2 x )} d x

\frac{d}{d x} (2 x^{3 x})

\frac{\partial}{\partial x} (\frac{1}{2} (x - y)^{2})

What is the derivative of x^{4/5}(x-2^2) ?
The derivative of x^{4/5}(x-2^2) is (14x^2-36x+16)/(5x^{1/5)}
What is the first derivative of x^{4/5}(x-2^2) ?
The first derivative of x^{4/5}(x-2^2) is (14x^2-36x+16)/(5x^{1/5)}